A functional-analytic and neural network approach to computer-interactive mathematics instruction and assessment.

摘要

This project employed an artificial neural network (a variation of Kohonen's self-organizing map, or SOM) in conjunction with Ninness et al.'s diagnostic computer-interactive mathematical software to resolve learning problems that occur during computer-interactive and traditional instruction. Following pretesting and a presentation regarding rules that govern mathematical relations pertaining to transformation of algebraic and trigonometric functions, participants completed a follow-up test. Subsequent training on transformation of mathematical functions was initiated using the software. In training A--B relations, standard formulae served as samples, and factored formulae as comparisons. In training B--C relations, factored formulae served as samples, and graphs as comparisons. Upon demonstration of combinatorial entailment (an understanding of the relationships between [C] and [A]), participants responded to 40 novel formulae. Participant error patterns were analyzed with Ninness et al.'s version of the SOM.